In the given figure , A and B are the centres of two circles having radii 5 cm and 3 cm respectively and intersecting at point P and Q respectively . If AB `=` 4 cm then the length of common chord PQ is

Options

A. 3 cm
B. 6 cm
C. 7.5 cm
D. 9 cm

Answer

B

Explanation

We know that the line joining their centres is the perpendicular bisector of the common chord. Join AP.
Then, `AP = 5cm ,BP = 3 cm` and `AB = 4 cm`
And, `AP^(2) = bp^(2) + AB^(2) [ :' 5^(2) = 3^(2) +4^(2)]`
`:. Delta ABP ` is right -angles and `PQ = 2 xx BP = (2 xx 3) cm = 6 cm`